Non-Categorical Syllogisms

A syllogism missing one of the propositions: John will never get a good job because he didn’t graduate.

To formulate a syllogism, find the conclusion, then the major, minor and middle terms: Those who did not graduate will not get a good job. John did not graduate. Therefore, John will not get a good job.

Sorites

a series of syllogisms without conclusions.

Progressive (Aristotelian) Sorites

First premise contains the Subject:

Every man is an animal.

Every animal is a living thing.

Every living thing is a substance.

Every substance is an existing thing. Therefore, every man is an existing.

vs.

Every man is an animal.

Every animal is a living thing.

Therefore, every man is a living thing. etc.

Rules: Only the first premise may be particular, and only the last negative.

Regressive (Goclenian) Sorites

First premise contains the Predicate:

Every substance is an existing thing.

Every living thing is a substance.

Every animal is a living thing.

Every man is an animal.

Therefore, every man is an existing thing.

Rules: Only the first premise may be negative, and only the last particular.

The Epicheirema

a syllogism with a causal premise (a “double syllogism”)

Every doctor is smart because they all study hard.

Lenny is a doctor.

Therefore, Lenny is smart.

This is actually two syllogisms:

Everyone who studies hard is smart.

Doctors study hard.

Therefore, doctors are smart.

+

Every doctor is smart.

Lenny is a doctor.

Therefore, Lenny is smart.

Compound Syllogisms: Conditional Syllogisms

the first proposition contains an “if…then” statement:

If Socrates is eating, then he exists. Socrates is eating.

Therefore, Socrates exists.

The antecedent must be affirmed or the consequent denied for the conclusion to be affected. There must be a necessary connection between antecedent and consequent.

Compound Syllogisms: Disjunctive Syllogisms

the first proposition contains an “either…or” statement:

Strong disjunct (cannot both be true):

The number 4 must be either even or odd. The number 4 is not odd.

Therefore, the number 4 is even.

Weak disjunct (both can be true):

Either Socrates is walking or talking.

Socrates is not walking.

Therefore he is talking.

Compound Syllogisms: The Dilemma

- the first proposition contains two contradictories:

No whole number can be both odd and even. This whole number is not even.

Therefore, this whole number is odd

The Dilemma:

Has two “horns” either pointing to one conclusion or to two impossibilities.

Either A or B.

If A then C.

If B then C.

Therefore, C.

or:

Either A or B.

If A then C.

If B then D.

Therefore either C or D.

Ways out of a Dilemma:

1. Escaping between the horns - discovering a third possibility.

2. Taking the dilemma by the horns - denying one of the possibilities.